I think you're mixing terms.
Parcel numbers represent the tax assessor's record keeping system. The first set of numbers might be the Map Book number, the second set of numbers would be the particular page in that book. The last set of numbers would be the assessor's lot number on that page in that book (note: this number may be different than the original subdivision lot number).
You can also identify the property by legal description which may be in metes and bounds (Starting at the iron pipe at the NW corner of Lot 25 in Section 1, Range 25, Township blah, blah, blah, proceed in a northerly direction 125.5 feet thence easterly 250 feet, thence southerly 125.5 thence westerly to the point of beginning) or subdivision lots and blocks (Lot 25, tract 15, in Gomer's Acres, subdivision 3).